Question

Points A and B are at `(3 ,7 )` and `(4 ,2 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` and dilated about point C by a factor of `2`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(-10,-16)`

Explanation:

`"under a counterclockwise rotation about the origin of "pi`

`• " a point "(x,y)to(-x,-y)`

`rArrA(3,7)toA'(-3,-7)" where A' is the image of A"`

`rArrvec(CB)=color(red)(2)vec(CA')`

`rArrulb-ulc=2(ula'-ulc)`

`rArrulb-ulc=2ula'-2ulc`

`rArrulc=2ula'-ulb`

`color(white)(rArrulc)=2((-3),(-7))-((4),(2))`

`color(white)(rArrulc)=((-6),(-14))-((4),(2))=((-10),(-16))`

`rArrC=(-10,-16)`